Achieving improved performance without sacrificing discretization accuracy requires an infrastructure that is consistent in the error metrics of the decoded data and an algorithm that remains efficient in the limit of large number of parallel tasks. In this paper, we will utilize domain decomposition (DD) techniques [1]} with data partitioning strategies to produce scalable MFA computation algorithms tha minimizes the reconstruction error when reproducing a given dataset. In such partitioned analysis, it is imperative to ensure that the continuity of the encoded and decoded data across subdomain interfaces is maintained, and remain consistent with the degree of underlying expansion bases used in MFA [2]}. This is due to the fact that independently computing MFA approximations in individual subdomains do not guarantee even \(C^0\)  regularity in either the MFA space or in the reconstructed data.
In order to tackle this issue, we rely on an iterative Schwarz-type DD scheme to ensure that continuity is enforced, and the overall error stays bounded as the number of subdomains are increased (or as the subdomain size decreases).
